99% of action cameras aren't very good for documenting bicycling. The battery life is the major limitation, since you would want to have the camera running continuously.
So either you need an external battery or something like a Fly12. The GoPro Session is a great camera. For the price, it's incredible. It does an excellent job dealing with sunlight and other bright sources.
Also, you aren't going to get any license plates in the dark. The headlights saturate the camera and you won't catch the plate.